Determine vector space with operations


Problem:

A vector space V

Please help with the following problem.

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Determine if the set R^2 (the real plane) is a vector space with operations defined by the following:

Addition: (a,b)+(c,d)=(a+c,b+d)

Scalar Multiplication: k(a,b)=(0,0)

Prove your answer. If this structure is not a vector space, state all the axioms of a vector space which are not satisfied and explain your answer.

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Mathematics: Determine vector space with operations
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